Many financial assets are valued based on indices that are multiplicative spreads over underlying indices. For example, many financial assets are valued based on the BMA Municipal Swap Index (“the BMA rate”). The BMA rate is an indicator of the market interest rate for tax-exempt municipal bonds issued by state and local governments. The BMA rate can be expressed as the appropriate LIBOR rate multiplied by a ratio.
Most existing models of the BMA rate and/or the ratio are based on the theory that the BMA rate is nothing more than the LIBOR rate corrected for the tax exempt status of municipal bonds in the United States. According to that theory, when the top marginal tax rate in the United States is 35%, the ratio of the BMA rate over LIBOR should be approximately 65%, (e.g., 100% minus 35% of the LIBOR rate). This leads to the theoretical assumptions that: (1) the ratio of BMA over LIBOR is constant; and (2) the volatility of BMA is equal to the volatility of LIBOR. In practice, however, there are significant conditions under which neither of these assumptions hold true. Accordingly, existing models are incapable of accurately modeling the BMA rate or the ratio of the BMA rate over LIBOR.